Stereograjphic and Gnomonic Projections. 



211 



through m!" and c at x, and that through m and d (through d 

 parallel to m m ,f , since m and m" are at infinity) at y. Next 

 imagine the points x and y transposed as in figure 1 to x' and 

 y', which latter .points, however, are located at infinity : This 

 transposition is clone by locating first the so-called Winhel- 

 punkt, W, of Goldschmidt, 10° from c in figure 7, and as in 

 figure 1, 90° from a point B, which is an equal number of 



Aatoo 



3c!atoo 



m 



.90° 



Figures 7 to 9. Development of a plan and parallel- perspective figure of 

 barite, orthorhombic system, from a gnomonic projection. 



degrees from ^and A' (compare figure 6). Of the three methods 

 given on pages 208 and 209 for transposing x and y to x' and 

 y', the third may be easily applied in the gnomonic projection. 

 Great circles, or straight lines, through W and x and TFand 

 y, figure '7, if continued to infinity, would determine x' and y f , 

 which is accomplished by drawing lines jmrallel to Wx and Wy 

 through the center. It is not necessary, however, to draw the 

 lines Wx and Wy, nor the parallel lines through the center ; 

 all that is needed to find the directions of the edges m!" a. g 

 and 7n /\ d is to lay a straight edge from TTto x, respectively 

 W to y, and with a 90° triangle transpose the directions to 

 figure 9, as indicated in the drawings. The principles are 

 exactly the same as worked out for the interrelations of figures 

 1 and 3. As in the case of the stereographic projection, it is 



